S3E38. What mathematicians do all day or Euler-Poisson integral evaluation via the Squeeze Theorem

In this episode we expand our viewers' intellectual horizon by evaluating the Euler-Poisson or the Gaussian integral via the Squeeze Theorem. An integral part of the very fabric of a proper mathematical eduction should be the cultural habit of fixing a problem and trying to generate as many different enough solutions for that problem as one can muster. Why. Because during the time that we spend searching for various solutions of a fixed problem our mind operates in the mode that is isomorphic to the mode in which the mind of a practicing mathematician operates when he or she acts in his or her professional capacity. This episode is precisely a story of an alternative solution to a problem that does not use the "traditional" integration techniques but, rather, appeals to the fact that every definite Riemann integral, proper or improper, at its raw technical essence, is a limit.